Block #428,438

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/4/2014, 2:15:33 AM · Difficulty 10.3463 · 6,379,743 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

087bf3868213b06ed5b422a5affc95888528a072f9d6b7625e98d291c4538b0e

View on Chainz ↗

Height

#428,438

Difficulty

10.346339

Transactions

Size

893 B

Version

Bits

0a58a9b3

Nonce

1,941

Timestamp

3/4/2014, 2:15:33 AM

Confirmations

6,379,743

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

bfd4023b7af72e469952d93306aff2f9bcd37847997879b1755de3b08bcb9c04

Transactions (3)

Coinbase35ec6f07ef4b0a…774fb4b2b60dc0

1 in → 1 out9.3500 XPM101 B

ASXb8Msj…BxGf64iZ

628ab0c55ee7b0…82f2c886baf1a8

1 in → 2 out38.0332 XPM225 B

AH2SoQYk…9b3G4uuR ATck3wBV…J2Sv9hxj

ee704ead8f57cd…2d62428f53e2df

2 in → 7 out18.5900 XPM476 B

AeKNrjNj…1NEq95Ta AUAVprvR…Q7nUDqV9 ATk9pefi…MKseqp2B AUF1So9U…9k1XHL4c AW6FdqAF…mbtgXE2r

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.201 × 10⁹⁶(97-digit number)

22013578018126313944…45994324625641695419

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.201 × 10⁹⁶(97-digit number)

22013578018126313944…45994324625641695419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.201 × 10⁹⁶(97-digit number)

22013578018126313944…45994324625641695421

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

4.402 × 10⁹⁶(97-digit number)

44027156036252627888…91988649251283390839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.402 × 10⁹⁶(97-digit number)

44027156036252627888…91988649251283390841

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

8.805 × 10⁹⁶(97-digit number)

88054312072505255777…83977298502566781679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.805 × 10⁹⁶(97-digit number)

88054312072505255777…83977298502566781681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

1.761 × 10⁹⁷(98-digit number)

17610862414501051155…67954597005133563359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.761 × 10⁹⁷(98-digit number)

17610862414501051155…67954597005133563361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

3.522 × 10⁹⁷(98-digit number)

35221724829002102311…35909194010267126719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.522 × 10⁹⁷(98-digit number)

35221724829002102311…35909194010267126721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer

Block #428,438

Cookie Preferences